Relationship between hooke law and young modulus of concrete

Young's modulus - Wikipedia

relationship between hooke law and young modulus of concrete

[link] shows the Hooke's law relationship between the extension \Delta L Tensile strength is the breaking stress that will cause permanent deformation or fracture .. The shear moduli for concrete and brick are very small; they are too highly. Young's modulus or Young modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain Young's modulus represents the factor of proportionality in Hooke's law, which Other such materials include wood and reinforced concrete . ratio of stress over strain [3]. In mechanics, Hooke's law of elasticity is an estimation that states that the amount of strain is linearly related to the stress [4].

Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear.

Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear.

Hooke's Law and Modulus of Elasticity

However, this is not an absolute classification: For example, as the linear theory implies reversibilityit would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.

In solid mechanicsthe slope of the stress—strain curve at any point is called the tangent modulus. It can be experimentally determined from the slope of a stress—strain curve created during tensile tests conducted on a sample of the material. Bend a bar or plate. Poisson's ratio governs the curvature in a direction perpendicular to the direction of bending. This "anticlastic curvature" is easily seen in the bending of a rubber eraser.

Stress, Strain and Hooke's Law - Lesson - TeachEngineering

Shown here is bending, by a moment applied to opposite edges, of a honeycomb with hexagonal cells. Since the honeycomb is anisotropic, the Poisson's ratio need not lie within the above range.

relationship between hooke law and young modulus of concrete

Poisson's ratio and anisotropy. In anisotropic solids including single crystals, honeycombs, and fibrous composites, physical properties, including Poisson's ratio and elastic moduli, depend on direction. Poisson's ratio can have positive or negative values of arbitrarily large magnitude in anisotropic materials. For orthotropic materials, Poisson's ratio is bounded by the ratio of Young's moduli E as follows.

Poisson's ratio in viscoelastic materials The Poisson's ratio in a viscoelastic material is time dependent in the context of transient tests such as creep and stress relaxation.

  • Hooke’s Law and Modulus of Elasticity

If the deformation is sinusoidal in time, Poisson's ratio may depend on frequency, and may have an associated phase angle. Specifically, the transverse strain may be out of phase with the longitudinal strain in a viscoelastic solid.

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Young's modulus

Poisson's ratio and phase transformations Poisson's ratio can vary substantially in the vicinity of a phase transformation. Typically the bulk modulus softens near a phase transformation but the shear modulus does not change much. The Poisson's ratio then decreases in the vicinity of a phase transformation and can attain negative values.

Phase transformations are discussed further on the linked page. Poisson's ratio, waves and deformation The Poisson's ratio of a material influences the speed of propagation and reflection of stress waves. In geological applications, the ratio of compressional to shear wave speed is important in inferring the nature of the rock deep in the Earth.

This wave speed ratio depends on Poisson's ratio. Poisson's ratio also affects the decay of stress with distance according to Saint Venant's principle, and the distribution of stress around holes and cracks. Analysis of effect of Poisson's ratio on compression of a layer. What about the effect of Poisson's ratio on constrained compression in the 1 or x direction? Constrained compression means that the Poisson effect is restrained from occurring. This could be done by side walls in an experiment.

Young's modulus and Hooke's Law

The quiz serves as a formative assessment while the next lesson's Go Public phase provides a summative assessment. Lecture Information In the late s, Robert Hooke stated that "The power of any springy body is in the same proportion with the extension.

The law is explained by a direct proportionality between a spring's compression or expansion and the restoring force which ensues. This law is valid within the elastic limit of a linear spring, when acting along a frictionless surface. Extending Hooke's exploration of springs, it becomes apparent that most materials act like springs with force being directly proportional to displacement.

But as compared to springs, other materials possess an area which must be accounted for. We will now explore the measures of stress and strain. The SI unit for stress is pascals Pa which is equal to 1 Newton per square meter. The Psi is an alternative unit which expresses pounds per square inch.

relationship between hooke law and young modulus of concrete

The units of stress are equal to the units of pressure which is also a measure of force per unit area.